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TECHNICAL PAPERS

Modeling Vibratory Drilling Dynamics

[+] Author and Article Information
Stephen A. Batzer

Mechanical Engineering Department, University of Arkansas, Fayetteville, AR 72701Batzer@engr.uark.edu

Alexander M. Gouskov

Department of Applied Mechanics, Bauman Moscow State Technical University, Moscow, Russiagouskov@rk5.bmstu.ru

Sergey A. Voronov

Department of Applied Mechanics, Bauman Moscow State Technical University, Moscow, RussiaVoronov@rk5.bmstu.ru

J. Vib. Acoust 123(4), 435-443 (Apr 01, 2001) (9 pages) doi:10.1115/1.1387024 History: Received February 01, 2000; Revised April 01, 2001
Copyright © 2001 by ASME
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References

Armarego, E. J. A., and Brown, R. H., 1977, The Machining of Metals, Mashinostroenie, Moscow, p. 325.
Gouskov, A. M., Svetlitsky, V. A., and Voronov, S. A., 1979, “Lateral Auto Vibration Excitation of Deep Hole Drill,” Collection of Papers Raschety na Prochnost, Mashinostroenie, Moscow, No. 20, pp. 172–182.
Hanna,  N. H., and Tobias,  S. A., 1974, “A Theory of Nonlinear Regenerative Chatter,” ASME J. Ind., 96, 247–255.
Marui,  E., Hashimoto,  M., and Kato,  S., 1995, “Regenerative Chatter Vibration Occurring in Turning with Different Side Cutting Edge Angles,” ASME J. Ind., 117, pp. 551–558.
Stepan, G., and Kalmar-Nagy, T., 1997, “Nonlinear Regenerative Machine Tool Vibrations,” Proceedings of the 1997 ASME Design Engineering Technical Conference, 16th Biennial Conference on Mechanical Vibration and Noise, ASME, Sacramento, DETC/VIB-4021, pp. 1–11.
Poduraev, V. N., 1970, Cutting with Vibrations, Mashinostroenie, Moscow, p. 351.
Kumabe, D., 1985, Vibratory Cutting, Mashinostroenie, Moscow, p. 424.
Poduraev, V. N., and Kibalchenko, A. V., 1993, The Technology of Defense Industry for Manufacturing of Customer Goods, Moscow, Rosconversia, p. 528.
Bayley, P. V., Metzler, S. A., Schaut, A. J., and Young, K. A., 2000, “Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Comparison to Test,” Proceedings of the ASME, MED, Vol. 11, pp. 899–908.
Gouskov, A. M., Voronov, S. A., and Nikitin, A. S., 1992, “Stochastic Regimes in Technologic Cutting Processes,” Proceedings of the 2nd International Scientific Technical Conference, Actual Problems of Fundamental Science, Technosphera Inform, Bauman Moscow State Technical University Press, Moscow, Vol. 2, pp. B2–B5.
Stephenson, D. A., and Agapiou, J. S., 1997, Metal Cutting Theory and Practice, Marcel Decker, New York.
Norkin, S. B., 1965, Second Order Differential Equations with Lag Argument, Nauka, Moscow, p. 355.
Hale, J., 1984, Theory of Functional Differential Equations, Mir, Moscow, p. 421.
Kalmar-Nagy, T., and Pratt, J. R., 1999, “Experimental and Analytical Investigation of the Subcritical Instability in Metal Cutting,” Proceedings of the 1999 Design Engineering Technical Conference. 17th ASME Biennial Conference on Mechanical Vibration and Noise, Las Vegas, DETC/VIB-8060, pp. 1–9.

Figures

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Vibratory drilling setup
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Forces and displacements of drilling model
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Example Bifurcation Diagrams for base system of parameters. Bifurcation diagrams for undeformed chip thickness β, tool displacements η1 and workpiece η2, and forces NC,N10 and N23 as a function of cutting velocity VC/VCB.
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Graphs Λ(τ), NC(τ) and Amplitude-Frequency Characteristics of NC for VC/VCB=1.5, ψ=0.352
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Graphs Λ(τ), NC(τ) and Amplitude-Frequency Characteristics of NC for VC/VCB=2.5, ψ=0.561
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Graphs Λ(τ), NC(τ) and Amplitude-Frequency Characteristics of NC for VC/VCB=3.5, ψ=0.752
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Bifurcation diagram of undeformed chip thickness β and tool displacement amplitude η1 dependent on σLLB
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Results of Tool Exit Modeling. Variation in time chip thickness β(τ), tool displacement η(τ), forces NC(τ) and N10(τ), hole depth Λ(τ) and Λ(τ−.5) for two cutting edges and phase map of tool motion (η̇1−η1).
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Bifurcation diagrams of β, NC1 and N10 dependent on frequency p in case of ζ10=0.05,m1/m1B=2,k10/k10B=2 and α0=0.1
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Bifurcation diagrams of β and f dependent on frequency p in case of ζ10=0.05,m1/m1B=2,k10/k10B=2 and α0=0.3
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Bifurcation diagrams of NC and N10 dependent on tool fixture stiffness k10 and variation of parameters of cutting continuity ψ and frequency of chip element formation f on k10
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Variation in time of chip thickness β and given motion of tool holder η00 sin 2πpτ and shape of chip for two values of tool holder stiffness k10/k10B=1.5 and k10/k10B=2.5

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